Download of refraction - Mrs. Brenner`s Biology

PHYSICS
Principles and Problems
Chapter 18: Refraction and Lenses
CHAPTER
18
Refraction and Lenses
BIG IDEA
Lenses refract light and create images.
CHAPTER
18
Table Of Contents
Section 18.1
Refraction of Light
Section 18.2
Convex and Concave Lenses
Section 18.3
Application of Lenses
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SECTION
Refraction of Light
18.1
MAIN IDEA
The amount of refraction at a boundary depends on the
indices of refraction of the two mediums and the angle of
incidence.
Essential Questions
•
What is Snell’s law of refraction?
•
What is the meaning of the index of refraction?
•
How does total internal reflection occur?
•
How does refraction cause various optical effects?
SECTION
Refraction of Light
18.1
Review Vocabulary
• refraction the change in direction of waves at the
boundary between two different mediums
New Vocabulary
•
•
•
•
Index of refraction
Critical angle
Total internal reflection
Dispersion
SECTION
18.1
Refraction of Light
Light and Boundaries
• When light encounters a transparent or
translucent medium, some light is reflected from
the surface of the medium and some is
transmitted through the medium.
• Recall that when light crosses a boundary
between two mediums, it bends. A phenomenon
called refraction.
SECTION
18.1
Refraction of Light
Light and Boundaries (cont.)
• Look at the figure below: Identical rays of light start in
air and pass into three different mediums at the same
angle.
• What do you notice about the light rays after they
cross the boundaries?
SECTION
18.1
Refraction of Light
Light and Boundaries (cont.)
• The light rays bend more when traveling from air
to diamond than from air to water or air to glass
because this phenomenon depends on properties
of the mediums that the light rays are traveling
from and into.
• What do you think the relationship is between the
angle of the light as it crosses the boundary
between mediums and refraction?
SECTION
18.1
Refraction of Light
Snell’s Law of Refraction
• When you shine a narrow beam of light at the surface of a
piece of glass, it bends as it crosses the boundary from air
to glass.
• The bending of light,
called refraction, was
first studied by René
Descartes and Willebrord
Snell around the time of
Kepler and Galileo.
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SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
• The angle of incidence, θ1, is the angle at which
the light ray strikes the surface.
• It is measured from
the normal to the
surface.
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SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
• The angle of refraction, θ2, is the angle at which
the transmitted light leaves the surface.
• It also is measured
with respect to the
normal.
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SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
• Snell found that when light went from air into a transparent
substance, the sines of the angles were related by the
equation sin θ1/sin θ2 = n.
• Here, n is a constant that depends on the substance, not
on the angles, and is called the index of refraction.
• The relationship found by Snell is also valid when light
goes across a boundary between any two materials.
SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
Snell’s Law of Refraction
• According to Snell’s Law of Refraction, the
product of the index of refraction of the first
medium and the sine of the angle of incidence is
equal to the product of the index of refraction of
the second medium and the sine of the angle of
refraction.
SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
• When light goes from air to glass, it moves from a
material with a lower index of refraction to one with a
higher index of refraction. That is, n1 < n2.
• To keep the two sides of the equation equal, one must
have sin θ1 > sin θ2.
• The light beam is bent toward the normal to the
surface.
SECTION
18.1
Refraction of Light
Snell’s Law of Refraction (cont.)
• When light travels from glass to air it moves from
material having a higher index of refraction to one with a
lower index. In this case, n1 > n2.
• To keep the two sides of the equation equal one must
have sin θ1 < sin θ2.
• The light is bent away from the normal.
• Note that the direction of the ray when it leaves the
glass is the same as it was before it struck the glass,
but it is shifted from its original position.
SECTION
18.1
Refraction of Light
Angle of Refraction
A light beam in air hits a sheet of float glass at an
angle of 30.0°. What is the angle of refraction of the
light ray?
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Step 1: Analyze and Sketch the Problem
• Make a sketch of the air and crown glass
boundary.
• Draw a ray diagram.
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Identify the known and unknown variables.
Known:
Unknown:
θ1 = 30.0º
θ2 = ?
n1 = 1.00
n2 = 1.52
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Step 2: Solve for the Unknown
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Use Snell’s law to solve for the sine of the angle of
refraction.
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Substitute n1 = 1.00, n2 = 1.52, θ1 = 30.0°
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Step 3: Evaluate the Answer
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
Are the units correct?
Angles are expressed in degrees.
Is the magnitude realistic?
The index of refraction, n2, is greater than the
index of refraction, n1. Therefore, the angle of
refraction, θ2, must be less than the angle of
incidence, θ1.
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
The steps covered were:
Step 1: Analyze and Sketch the Problem
Make a sketch of the beam moving from the air
to the crown glass.
Draw a ray diagram.
SECTION
18.1
Refraction of Light
Angle of Refraction (cont.)
The steps covered were:
Step 2: Solve for the Unknown
Use Snell’s law to solve for the sine of the angle
of refraction.
Step 3: Evaluate the Answer
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction
• The wave relationship for light traveling through a
vacuum, λ = c/f, can be rewritten as λ = v/f, where
v is the speed of light in any medium, and λ is the
wavelength.
• The frequency of light, f, does not change when it
crosses a boundary.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• That is, the number of oscillations per second that
arrive at a boundary is the same as the number
that leave the boundary and transmit through the
refracting medium.
• So, the wavelength of light, λ, must decrease
when light slows down. Wavelength in a medium
is shorter than wavelength in a vacuum.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• The diagram shows a beam of
light as being made up of a
series of parallel, straight wave
fronts.
• Each wave front represents the
crest of a wave and is
perpendicular to the direction of
the beam.
• The beam strikes the surface at
an angle, θ1.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• Consider the triangle PQR.
• Because the wave fronts are
perpendicular to the direction
of the beam, PQR is a right
angle and QRP is equal
to θ1.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• Sin θ1 is equal to the
distance between P and Q
divided by the distance
between P and R.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• The angle of refraction, θ2, can
be related in a similar way to the
triangle PSR. In this case:
• By taking the ratio of the sines of
the two angles,
is canceled,
leaving the following equation:
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
•
•
.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
•
• Using λ = v/f in the above equation and canceling the
common factor of f, the equation is rewritten as follows:
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• Snell’s law also can be written as a ratio of the
sines of the angles of incidence and refraction.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• Using the transitive property of equality, the previous two
equations lead to the following equation:
• In a vacuum, n = 1 and v = c.
• If the medium is a vacuum, then the equation is simplified
to an equation that relates the index of refraction to the
speed of light in a medium.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
Index of Refraction
• The index of refraction of a medium is equal to the
speed of light in a vacuum divided by the speed of
light in the medium.
• This definition of the index of refraction can be
used to find the wavelength of light in a medium.
SECTION
18.1
Refraction of Light
The Meaning of the Index of Refraction (cont.)
• In a medium with an index of refraction n, the speed
of light is given by v = c/n.
• The wavelength of the light in a vacuum is λ0 = c/f.
• Solve for frequency, and substitute f = c/λ0 and
v = c/n into λ = v/f. λ = (c/n)/(c/λ0) = λ0/n, and thus the
wavelength of light in a medium is smaller than the
wavelength in a vacuum.
SECTION
18.1
Refraction of Light
Total Internal Reflection
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SECTION
18.1
Refraction of Light
Total Internal Reflection (cont.)
• To construct an equation for the critical angle of any
boundary, you can use Snell’s law and substitute θ1 = θc
and θ2 = 90.0°.
Critical Angle for Total Internal Reflection
• The sine of the critical angle is equal to the index of
refraction of the refracting medium divided by the index of
refraction of the incident medium.
SECTION
18.1
Refraction of Light
Total Internal Reflection (cont.)
• Total internal reflection causes some curious effects.
• Suppose that you are looking up at the surface from
underwater in a calm pool.
• You might see an upside-down reflection of another
nearby object that also is underwater or a reflection of
the bottom of the pool itself.
• The surface of the water acts like a mirror.
SECTION
18.1
Refraction of Light
Total Internal Reflection (cont.)
• Likewise, when you are standing on the side of a pool, it is
possible for things below the surface of the water in the
pool to not be visible to you.
• When a swimmer is underwater, near the surface, and on
the opposite side of the pool from you, you might not see
him or her.
• This is because the light from his or her body does not
transmit from the water into the air, but is reflected.
SECTION
18.1
Refraction of Light
Total Internal Reflection (cont.)
• Optical fibers are an important technical application of total
internal reflection.
• The light traveling through the transparent fiber always hits
the internal boundary of the optical fiber at an angle
greater than the critical angle, so all of the light is reflected
and none of the light is transmitted through the boundary.
• Thus, the light maintains its intensity over the distance of
the fiber.
SECTION
18.1
Refraction of Light
Mirages
• On a hot summer day, as you drive down a road, you
see what appears to be the reflection of an oncoming
car in a pool of water.
• The pool, however, disappears as you approach it.
SECTION
18.1
Refraction of Light
Mirages (cont.)
• The mirage is the result of the Sun heating the road.
• The hot road heats the air above it and produces a
thermal layering of air that causes light traveling toward
the road to gradually bend upward.
• This makes the light appear to be coming from a reflection
in a pool.
SECTION
18.1
Refraction of Light
Mirages (cont.)
• As light from a distant object travels downward
toward the road, the index of refraction of the air
decreases as the air gets hotter, but the
temperature change is gradual.
SECTION
18.1
Refraction of Light
Mirages (cont.)
• In the case of a mirage, the Huygens’ wavelets
closer to the ground travel faster than those
higher up, causing the wave fronts to gradually
turn upward.
SECTION
18.1
Refraction of Light
Mirages (cont.)
• A similar phenomenon, called a superior mirage,
occurs when a reflection of a distant boat appears
above the boat.
• The water keeps the air that is closer to its surface
cooler.
SECTION
18.1
Refraction of Light
Dispersion of Light
• The speed of light in a medium is determined by
interactions between the light and the atoms that
make up the medium.
• Temperature and pressure are related to the
energy of particles on the atomic level.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• The speed of light, and therefore, the index of
refraction for a gaseous medium, can change
slightly with temperature.
• In addition, the speed of light and the index of
refraction vary for different wavelengths of light in
the same liquid or solid medium.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• White light separates into
a spectrum of colors
when it passes through a
glass prism. This
phenomenon is called
dispersion.
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SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• If you look carefully at the
light that passes through a
prism, you will notice that
violet is refracted more
than red.
• This occurs because the
speed of violet light
through glass is less than
the speed of red light
through glass.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Violet light has a higher frequency than red light,
which causes it to interact differently with the
atoms of the glass.
• This results in glass having a slightly higher index
of refraction for violet light than it has for red light.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• A prism is not the only means of dispersing light.
• A rainbow is a spectrum formed when sunlight is
dispersed by water droplets in the atmosphere.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Sunlight that falls on a water droplet is refracted.
• Because of dispersion, each color is refracted at a
slightly different angle.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• At the back surface of the droplet, some of the
light undergoes internal reflection.
• On the way out of the droplet, the light once again
is refracted and dispersed.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Although each droplet produces a complete spectrum,
an observer positioned between the Sun and the rain
will see only a certain wavelength of light from each
droplet.
• The wavelength depends on
the relative positions of the
Sun, the droplet, and the
observer.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Because there are many droplets in the sky, a
complete spectrum is visible.
• The droplets reflecting red light make an angle of
42° in relation to the direction
of the Sun’s rays; the droplets
reflecting blue light make an
angle of 40°.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Sometimes, you can see a faint second-order
rainbow.
• The second rainbow is outside the first, is fainter,
and has the order of the
colors reversed.
• Light rays that are reflected
twice inside water droplets
produce this effect.
SECTION
18.1
Refraction of Light
Dispersion of Light (cont.)
• Very rarely, a third rainbow is visible outside the
second.
• What is your prediction about how many times
light is reflected in the water
droplets and the order of
appearance of the colors for
the third rainbow?
SECTION
18.1
Section Check
Why do the feet of a person standing still in a
swimming pool appear to move back and
forth?
A. because water is denser than air
B. because water is more viscous than air
C. because light changes direction as it passes into air
D. because light spreads as it passes from air to water
SECTION
18.1
Section Check
Answer
Reason: When light passes from one medium to
another, its path bends due to refraction. As
light waves travel along the surface of water,
the boundary between air and water moves
up and down, and tilts back and forth. The
path of light leaving the water shifts as the
boundary moves, causing objects under the
surface to appear to waver.
SECTION
18.1
Section Check
What happens when light traveling from a region of
a higher index of refraction to a region of a lower
index of refraction strikes the boundary at an angle
greater than the critical angle?
A. All light reflects back into the region of higher index of
refraction.
B. The refracted light ray lies along the boundary of the two
media.
C. The angle of refraction is less than the angle of
incidence.
D. All light is absorbed at the boundary.
SECTION
18.1
Section Check
Answer
Reason: Total internal reflection occurs when light
traveling from a region of higher index of
refraction to a region of lower index of
refraction strikes the boundary at an angle
greater than the critical angle such that all
light reflects back into the region of higher
index of refraction.
SECTION
18.1
Section Check
Explain why, if you are standing by the side of a pool,
you cannot see a swimmer who is underwater near the
surface, and on the opposite side of the pool.
A. This is because the light from the swimmer’s body refracts
along the boundary of air and water.
B. This is because the light from the swimmer’s body is not
transmitted from the water into the air, but is reflected back
into the water.
C. This is because the light from the swimmer’s body refracts on
the opposite side of the pool.
D. This is because the light from the swimmer’s body is partially
refracted and partially reflected.
SECTION
18.1
Section Check
Answer
Reason: The surface of water acts like a mirror.
Hence, when a swimmer is underwater,
the light from the swimmer’s body is not
transmitted from the water into the air, but
is reflected back into the water. Therefore,
we cannot see the swimmer from the
opposite side of the pool.
SECTION
18.2
Convex and Concave Lenses
MAIN IDEA
Lenses can be used to make enlarged and reduced images.
Essential Questions
•
How are real and virtual images formed by single convex
and concave lenses?
•
How can images formed by lenses be located and
described with ray diagrams and equations?
•
How can chromatic aberration be reduced?
SECTION
Convex and Concave Lenses
18.2
Review Vocabulary
• transparent a property of a medium that allows that
medium to transmit light and reflect a fraction of the
light, allowing objects to be seen clearly through it
New Vocabulary
•
•
•
•
Lens
Convex lens
Concave lens
Thin lens equation
• Chromatic aberration
• Achromatic lens
SECTION
18.2
Convex and Concave Lenses
Types of Lenses
• A lens is a piece of transparent material, such as
glass or plastic, that is used to focus light and
form an image.
• Each of a lens’s two faces might be either curved
or flat.
SECTION
18.2
Convex and Concave Lenses
Types of Lenses (cont.)
• The lens shown in the figure is called a convex lens
because it is thicker at the center than at the edges.
• A convex lens often is called
a converging lens because
when surrounded by material
with a lower index of
refraction, it refracts parallel
light rays so that the rays
meet at a point.
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SECTION
18.2
Convex and Concave Lenses
Types of Lenses (cont.)
• The lens shown in the figure is called a concave lens
because it is thinner in the middle than at the edges.
• A concave lens often is called
a diverging lens because
when surrounded by material
with a lower index of
refraction, rays passing
through it spread out.
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SECTION
18.2
Convex and Concave Lenses
Types of Lenses (cont.)
• When light passes through a lens, refraction occurs at the
two lens surfaces.
• Using Snell’s law and geometry, you can predict the paths
of rays passing through lenses.
• To simplify such problems, assume that all refraction
occurs on a plane, called the principal plane, that passes
through the center of the lens.
• This approximation, called the thin lens model, applies to
all the lenses that you will learn about in this section.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses
• Paper can be ignited by producing a real image of
the Sun on the paper.
• The rays of the Sun are almost exactly parallel
when they reach Earth.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• After being refracted by the
lens, the rays converge at
the focal point, F, of the
lens.
• The figure shows two focal
points, one on each side of
the lens.
• You could turn the lens
around, and it will work the
same.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
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SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• When an object is placed at the focal point of a convex
lens, the refracted rays will emerge in a parallel beam
and no image will be seen.
• When the object is brought closer to the lens, the rays
will diverge on the opposite side of the lens, and the
rays will appear to an observer to come from a spot on
the same side of the lens as the object.
• This is a virtual image that is upright and larger
compared to the object.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• The figure shows how a convex lens forms a virtual
image.
• The object is located between F and the lens.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• Ray 1, as usual, approaches the lens parallel to
the principal axis and is refracted through the
focal point, F.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• Ray 2 travels from the tip of the object, in the
direction it would have if it had started at F on the
object side of the lens.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• The dashed line from F to the object shows you
how to draw ray 2.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• Ray 2 leaves the lens parallel to the principal axis.
• Rays 1 and 2 diverge as they leave the lens.
• Thus, no real image is possible.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• Drawing sight lines for the two rays back to
their apparent intersection locates the virtual
image.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• It is on the same side of the lens as the object,
and it is upright and larger compared to the object.
SECTION
18.2
Convex and Concave Lenses
Convex Lenses (cont.)
• Note that the actual image is formed by light that passes
through the lens.
• But you can still determine the location of the image by
drawing rays that do not have to pass through the lens.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses
• A concave lens causes all rays to diverge.
• The figure shows how such a lens forms a virtual
image.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• Ray 1 approaches the lens parallel to the principal
axis, and leaves the lens along a line that extends
back through the focal point.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• Ray 2 approaches the lens as if it is going to pass
through the focal point on the opposite side, and
leaves the lens parallel to the principal axis.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• The sight lines of rays 1 and 2 intersect on the same side
of the lens as the object.
• Because the rays diverge, they produce a virtual image.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• The image is located at the point from where the
two rays apparently diverge.
• The image also is upright and smaller compared to
the object.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• This is true no matter how far from the lens the
object is located.
• The focal length of a concave lens is negative.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• When solving problems for concave lenses using
the thin lens equation, you should remember that
the sign convention for focal length is different
from that of convex lenses.
• If the focal point for a concave lens is 24 cm from
the lens, you should use the value
f = −24 cm in the thin lens equation.
SECTION
18.2
Convex and Concave Lenses
Concave Lenses (cont.)
• All images for a concave lens are virtual. Thus, if
an image distance is given as 20 cm from the
lens, then you should use di = −20 cm.
• The object position always will be positive.
SECTION
18.2
Convex and Concave Lenses
Lens Equations
• The problems that you will solve involve spherical
thin lenses, lenses that have faces with the same
curvature as a sphere.
• Based on the thin lens model, as well as the other
simplifications used in solving problems for
spherical mirrors, equations have been developed
that look exactly like the equations for spherical
mirrors.
SECTION
18.2
Convex and Concave Lenses
Lens Equations (cont.)
• The thin lens equation relates the focal length of
a spherical thin lens to the object position and the
image position.
• The inverse of the focal length of a spherical lens
is equal to the sum of the inverses of the image
position and the object position.
SECTION
18.2
Convex and Concave Lenses
Lens Equations (cont.)
• The magnification equation for spherical mirrors also can
be used for spherical thin lenses.
• It is used to determine the height and orientation of the
image formed by a spherical thin lens.
• The magnification of an object by a spherical lens, defined
as the image height divided by the object height, is equal
to the negative of the image position divided by the object
position.
SECTION
18.2
Convex and Concave Lenses
Lens Equations (cont.)
• It is important that you use the proper sign conventions
when using these equations.
• The table shows a comparison of the image position,
magnification, and type of image formed by single convex
and concave lenses when
an object is placed at
various object positions,
do, relative to the lens.
SECTION
18.2
Convex and Concave Lenses
Lens Equations (cont.)
• As with mirrors, the distance from the principal plane
of a lens to its focal point is the focal length, f.
• The focal length depends upon the shape of the lens
and the index of refraction of the lens material.
• Focal lengths and image positions can be negative.
• For lenses, virtual images are always on the same
side of the lens as the object, which means that the
image position is negative.
SECTION
18.2
Convex and Concave Lenses
Lens Equations (cont.)
• When the absolute value of a magnification is between
zero and one, the image is smaller than the object.
• Magnifications with absolute values greater than one
represent images that are larger than the objects.
• A negative magnification means the image is inverted
compared to the object.
• Notice that a concave lens produces only virtual images,
whereas a convex lens can produce real images or virtual
images.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens
An object is placed 32.0 cm from a convex lens
that has a focal length of 8.0 cm.
a. Where is the image?
b. If the object is 3.0 cm high, how tall is the
image?
c. What is the orientation of the image?
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Step 1: Analyze and Sketch the Problem
• Sketch the situation,
locating the object and
the lens.
• Draw the two principal
rays.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Identify the known and unknown variables.
Known:
Unknown:
xo = 32.0 cm
xi = ?
ho = 3.0 cm
hi = ?
f = 8.0 cm
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Step 2: Solve for the Unknown
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Use the thin lens equation to determine xi.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Substitute f = 8.0 cm, xo = 32.0 cm
11 cm away from the lens on the side opposite the
object
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Use the magnification equation and solve for image
height.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Substitute di = 11 cm, ho = 3.0 cm, xo = 32.0 cm
The negative sign means that the image is inverted.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Step 3: Evaluate the Answer
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
Are the units correct?
All are in centimeters.
Do the signs make sense?
Image position is positive (real image) and
image height is negative (inverted compared
to the object), which make sense for a convex
lens.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
The steps covered were:
Step 1: Analyze and Sketch the Problem
Sketch the situation, locating the object and the
lens.
Draw the two principal rays.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
The steps covered were:
Step 2: Solve for the Unknown
Use the thin lens equation to determine di.
Use the magnification equation and solve for
image height.
The negative sign in part b means that the
image is inverted.
SECTION
18.2
Convex and Concave Lenses
An Image Formed by a Convex Lens (cont.)
The steps covered were:
Step 3: Evaluate the Answer
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses
• Spherical lenses, just like spherical mirrors, have
intrinsic defects that cause problems with the focus
and color of images.
• Spherical lenses exhibit an aberration associated with
their spherical design, just as mirrors do.
• In addition, the dispersion of light through a spherical
lens causes an aberration that mirrors do not exhibit.
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• The model that you have used for drawing rays
through spherical lenses suggests that all parallel
rays focus at the same position.
• However, this is only an approximation.
• In reality, parallel rays that pass through the edges of
a spherical lens focus at positions different from those
of parallel rays that pass through the center.
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• This inability of a spherical lens to focus all parallel
rays to a single point is called spherical aberration.
• Making lens surfaces aspherical, such as in cameras,
eliminates spherical aberration.
• In high-precision instruments, many lenses, often five
or more, are used to form sharp, well-defined images.
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• Lenses have a second defect that mirrors do not have.
• A lens is like a prism, so different
wavelengths of light are refracted
at slightly different angles.
• Thus, the light that passes through
a lens, especially near the edges,
is slightly dispersed.
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• An object viewed through a lens appears to be
ringed with color.
• This effect is called chromatic aberration.
• The term chromatic comes from the Greek word
chromo, which means “color.”
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• Chromatic aberration is always present when a
single lens is used.
• However, this defect can be greatly reduced by an
achromatic lens, which is a system of two or more
lenses, such as a convex lens with a concave
lens, that have different indices of refraction.
SECTION
18.2
Convex and Concave Lenses
Defects of Spherical Lenses (cont.)
• Both lenses in the figure disperse light, but the
dispersion caused by the convex lens is almost
canceled by the dispersion caused by the
concave lens.
• The index of refraction of
the convex lens is chosen
so that the combination of
lenses still converges the
light.
SECTION
18.2
Section Check
What type of image does a convex lens produce, when
an object is placed at a distance greater than twice the
focal length of the lens?
A. A real image is produced that is inverted and smaller as
compared to the object.
B. A virtual image is produced that is smaller than the
object.
C. A real image is produced that is inverted and larger than
the object.
D. A real image is produced that is inverted and the same
size as the object.
SECTION
18.2
Section Check
Answer
Reason: For the purpose of locating the image, you only
need to use two rays. Ray 1 is parallel to the
principle axis. It refracts and passes through F on
the other side of the lens. Ray 2 passes through F
on its way to the lens.
SECTION
18.2
Section Check
What will be the position and size of the image when an
object is placed at a distance equal to twice the focal
length of a convex lens?
A. An inverted image bigger than the object will be
produced beyond 2F.
B. An inverted image smaller than the object will be
produced beyond 2F.
C. The image will be produced at infinity.
D. An inverted image having the same size as the object
will be produced at 2F.
SECTION
18.2
Section Check
Answer
Reason: If an object is placed at a distance equal to twice
the focal length of a convex lens, an inverted
image will be produced at 2F. The size of the
image will be the same as the size of the object as
shown in the following ray diagram.
SECTION
18.2
Section Check
What type of image is produced by a convex lens, when
the object is placed between F and 2F?
A. A real image is produced that is inverted and smaller
than the object.
B. A virtual image is produced that is smaller than the
object.
C. A real image is produced that is inverted and bigger than
the object.
D. A real image is produced that is inverted and the same
size as the object.
SECTION
18.2
Section Check
Answer
Reason: When an object is placed between F and 2F, a real
image is produced that is inverted and bigger than
the object. This is shown in the following figure.
SECTION
Application of Lenses
18.3
MAIN IDEA
People see objects that they could not otherwise see by
using lenses.
Essential Questions
•
How does the eye focus light to form an image?
•
What are nearsightedness and farsightedness and how
can eyeglass lenses correct these defects?
•
What are the characteristics of the optical systems in
some common optical instruments?
SECTION
18.3
Application of Lenses
Review Vocabulary
• Index of refraction for a medium, the ratio of the
speed of light in a vacuum to the speed of light in that
medium
New Vocabulary
• Nearsightedness
• Farsightedness
SECTION
18.3
Application of Lenses
Lenses in Eyes
• The properties that you have learned for the refraction
of light through lenses are used in almost every
optical instrument.
• In many cases, a combination of lenses and mirrors is
used to produce clear images of small or faraway
objects.
• Telescopes, binoculars, cameras, microscopes, and
even your eyes contain lenses.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• The eye is a fluid-filled, almost spherical vessel.
• Light that is emitted or reflected off an object travels into
the eye through the cornea.
• The light then passes through the lens and focuses onto
the retina that is at the back of the eye.
• Specialized cells on the retina
absorb this light and send
information about the image
along the optic nerve to the
brain.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• Because of its name, you might assume that the
lens of an eye is responsible for focusing light
onto the retina.
• In fact, light entering the eye is primarily focused
by the cornea because the air-cornea surface has
the greatest difference in indices of refraction.
• The lens is responsible for the fine focus that
allows you to clearly see both distant and nearby
objects.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• Using a process called accommodation, muscles
surrounding the lens can contract or relax, thereby
changing the shape of the lens.
• This, in turn, changes the focal length of the eye. When
the muscles are relaxed, the image of distant objects is
focused on the retina.
• When the muscles contract, the focal length is shortened,
and this allows images of closer objects to be focused on
the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• The eyes of many people do not focus sharp
images on the retina.
• Instead, images are focused either in front of the
retina or behind it.
• External lenses, in the form of eyeglasses or
contact lenses, are needed to adjust the focal
length and move images to the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• The figure shows the
condition of
nearsightedness, or
myopia, whereby the
focal length of the eye
is too short to focus
light on the retina.
• Images are formed in
front of the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• Concave lenses
correct this by
diverging light, thereby
increasing images’
distances from the
lens, and forming
images on the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• You also can see in the figure that
farsightedness, or hyperopia, is the condition in
which the focal length of the eye is too long.
• Images are, therefore,
formed past the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• A similar result is caused by the increasing
rigidity of the lenses in the eyes of people who
are more than about 45 years old.
• Their muscles cannot
shorten the focal length
enough to focus images of
close objects on the retina.
SECTION
18.3
Application of Lenses
Lenses in Eyes (cont.)
• For either defect, convex
lenses produce virtual
images farther from the eye
than the associated
objects.
• The image from the lens
becomes the object for the
eye, thereby correcting the
defect.
SECTION
18.3
Application of Lenses
Refracting Telescopes
• An astronomical refracting telescope uses lenses
to magnify distant objects. The figure shows the
optical system for a Keplerian telescope.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• Light from stars and other astronomical objects is
so far away that the rays can be considered
parallel.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• The parallel rays of light enter the objective
convex lens and are focused as a real image at
the focal point of the objective lens.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• The image is inverted compared to the object.
This image then becomes the object for the
convex lens of the eyepiece.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• Notice that the eyepiece lens is positioned so that
the focal point of the objective lens is between the
eyepiece lens and its focal point.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• This means that a virtual image is produced that
is upright and larger than the first image.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• However, because the first image was already
inverted, the final image is still inverted.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• For viewing astronomical objects, an image that is
inverted is acceptable.
SECTION
18.3
Application of Lenses
Refracting Telescopes (cont.)
• In a telescope, the convex lens of the eyepiece is
almost always an achromatic lens.
• An achromatic lens is a combination of lenses that
function as one lens.
• The combination of lenses eliminates the
peripheral colors, or chromatic aberration, that
can form on images.
SECTION
18.3
Application of Lenses
Cameras
• The figure shows the optical system used in a singlelens reflex camera.
• As light enters the camera, it
passes through an achromatic
lens. This lens system refracts
the light much like a single
convex lens would, forming an
image that is inverted on the
reflex mirror.
SECTION
18.3
Application of Lenses
Cameras (cont.)
• The image is reflected
upward to a prism that
redirects the light to the
viewfinder.
SECTION
18.3
Application of Lenses
Cameras (cont.)
• When the person holding the
camera takes a photograph,
he or she presses the shutterrelease button, which briefly
raises the mirror.
• The light, instead of being
diverted upward to the prism,
then travels along a straight
path to focus on the film.
SECTION
18.3
Application of Lenses
Microscopes
• Like a telescope, a microscope has both an objective
convex lens and a convex eyepiece.
• However, microscopes are
used to view small objects.
• The figure shows the optical
system used in a simple
compound microscope.
SECTION
18.3
Application of Lenses
Microscopes (cont.)
• The object is located between one and two focal lengths
from the objective lens.
• A real image is produced that
is inverted and larger than the
object.
• As with a telescope, this image
then becomes the object for the
eyepiece.
• This image is between the
eyepiece and its focal point.
SECTION
18.3
Application of Lenses
Microscopes (cont.)
• A virtual image is produced that is upright and
larger than the image of the objective lens.
• Thus, the viewer sees an
image that is inverted and
greatly larger than the
original object.
SECTION
18.3
Application of Lenses
Binoculars
• Binoculars, like telescopes,
produce magnified images
of faraway objects.
• Each side of the binoculars
is like a small telescope:
light enters a convex
objective lens, which inverts
the image.
SECTION
18.3
Application of Lenses
Binoculars (cont.)
• The light then travels
through two prisms that use
total internal reflection to
invert the image again, so
that the viewer sees an
image that is upright
compared to the object.
SECTION
18.3
Application of Lenses
Binoculars (cont.)
• The prisms also extend
the path along which
the light travels and
direct it toward the
eyepieces of the
binoculars.
SECTION
18.3
Application of Lenses
Binoculars (cont.)
• Just as the separation of
your two eyes gives you a
sense of three dimensions
and depth, the prisms allow
a greater separation of the
objective lenses, thereby
improving the
three-dimensional
view of a distant object.
SECTION
18.3
Section Check
Describe how the eyes focus light to form an
image.
SECTION
18.3
Section Check
Answer
Light entering the eye is primarily focused by the
cornea because the air-cornea surface has the
greatest difference in indices of refraction. The lens
is responsible for the fine focus that allows you to
see both distant and nearby objects clearly. Using a
process called accommodation, muscles
surrounding the lens can contract or relax, thereby
changing the shape of the lens. This, in turn,
changes the focal length of the eye.
SECTION
18.3
Section Check
Answer
When the muscles are relaxed, the image of distant
objects is focused on the retina. When the muscles
contract, the focal length is shortened, and this
allows images of closer objects to be focused on
the retina.
SECTION
18.3
Section Check
Describe the optical system in an astronomical
refracting telescope.
SECTION
18.3
Section Check
Answer
An astronomical refracting telescope uses lenses to
magnify distant objects.
Light from stars and other astronomical objects is
so far away that the rays can be considered
parallel. The parallel rays of light enter the objective
convex lens and are focused as a real image at the
focal point of the objective lens, Fo. The image is
inverted compared to the object.
SECTION
18.3
Section Check
Answer
Rays from this image then become the object for
the convex lens of the eyepiece. Notice that the
eyepiece lens is positioned so that the point Fo is
between the eyepiece lens and its focus. This
means that a virtual image is produced that is
upright and larger than the object. However,
because the image at Fo was inverted, the viewer
sees an image that is inverted.
SECTION
18.3
Section Check
Describe the optical system in a single-lens
reflex camera.
SECTION
18.3
Section Check
Answer
As light rays enter a camera, they pass through an
achromatic lens. This lens system refracts the light
much like a single convex lens would, forming an image
that is inverted on the reflex mirror. The image is
reflected upward to a prism that redirects the light to the
viewfinder. Pressing the shutter release button of a
camera briefly raises the mirror. The light, instead of
being diverted upward to the prism, then travels along a
straight path to focus on the film.
CHAPTER
Refraction and Lenses
18
Resources
Physics Online
Study Guide
Chapter Assessment Questions
Standardized Test Practice
SECTION
Refraction of Light
18.1
Study Guide
•
A beam of light refracts when it travels across a
boundary from one medium with an index of refraction
(n1) into a medium with a different index of refraction
(n2). Refraction is described by Snell’s law of
refraction.
n1 sin 1 = n2 sin 2
SECTION
Refraction of Light
18.1
Study Guide
• The speed of light in a medium is slower than the
speed of light in a vacuum. The ratio of the
speed of light in a vacuum (c) to the speed of
light in a medium (v) is the index of refraction (n)
of the medium.
SECTION
Refraction of Light
18.1
Study Guide
• When light traveling through a medium hits a
boundary with a medium of a smaller index of
refraction, if the angle of incidence exceeds the
critical angle (θc) the light will be reflected back
into the original medium by total internal
reflection. The indices of refraction for the
mediums determine the critical angle.
SECTION
Refraction of Light
18.1
Study Guide
• Optical effects such as mirages and rainbows are
the result of refraction. Mirages occur due to the
effect of temperature on n and rainbows occur
because refracted white light is dispersed.
SECTION
18.2
Convex and Concave Lenses
Study Guide
• A single convex lens produces a real image,
formed by converging light rays, when the object
is at the focal point or farther from the lens. A
single convex lens produces a virtual image,
formed by diverging light rays, when the object is
between the lens and the focal point. A single
concave lens always produces a virtual image,
formed by diverging light rays.
SECTION
18.2
Convex and Concave Lenses
Study Guide
• Ray diagrams use two rays to determine the
position, magnification, and orientation of an
image formed by a lens. The thin lens equation
provides the relationship between focal length
(f), object position (xo) and image position (xi).
The magnification (m) of an image by a lens is
defined by the magnification equation.
SECTION
18.2
Convex and Concave Lenses
Study Guide
•
All simple lenses have chromatic aberration.
Chromatic aberration is reduced by using a
combination of lenses with different indices of
refraction.
SECTION
Application of Lenses
18.3
Study Guide
• Differences in indices of refraction between air
and the cornea are primarily responsible for
focusing light in the eye.
• Nearsightedness is the inability to focus clearly
on distant objects. A concave lens corrects
nearsightedness. Farsightedness is the inability
to focus clearly on nearby objects. A convex lens
corrects farsightedness.
SECTION
Application of Lenses
18.3
Study Guide
• Optical instruments use combinations of lenses to
obtain clear images of small or distant objects.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
How does the light traveling through a
transparent fiber maintain its intensity over the
distance of the fiber?
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Answer: Optical fibers are an important technical
application of total internal reflection. The light traveling
through the transparent fiber always hits the internal
boundary of the optical fiber at an angle greater than
the critical angle, so all of the light is reflected and none
of the light is transmitted through the boundary. Thus,
the light maintains its intensity over the distance of the
fiber.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Which of the following properties of light
causes rainbows?
A. constructive interference of light
B. dispersion of light
C. diffraction of light
D. destructive interference of light
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Reason: A rainbow is a spectrum formed when
sunlight is dispersed by water droplets in
the atmosphere. Sunlight that falls on a
water droplet is refracted. Because of
dispersion, each color is refracted at a
slightly different angle.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Why do concave lenses produce only virtual
images that are upright and smaller compared
to the objects?
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Answer: A concave lens causes all rays to diverge.
The following figure shows how such a lens forms a
virtual image.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
Answer: Ray 1 approaches the lens parallel to the principal
axis. It leaves the lens along a line that extends back
through the focal length. Ray 2 approaches the lens as if it is
going to pass through the focal point on the opposite side,
and leaves the lens parallel to the principal axis. The sight
lines of rays 1 and 2 intersect on the same side of the lens
as the object. Because the rays diverge, they produce a
virtual image. The image is located at the point from where
the two rays apparently diverge. The image is upright and
smaller as compared to the object.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
An object is placed 30 cm from a convex lens
that has a focal length of 8 cm. What is the
image distance?
A.
C.
B.
D.
CHAPTER
Refraction and Lenses
18
Chapter Assessment
Reason: The thin lens equation is:
The reciprocal of the focal length of a spherical
mirror is equal to the sum of the reciprocal of the
image position and the object position.
Then,
.
CHAPTER
18
Refraction and Lenses
Chapter Assessment
What are nearsightedness and farsightedness? How can
these defects be corrected?
Answer: A nearsighted person cannot see distant objects
clearly, because images are focused in front of the retina. A
concave lens corrects this defect.
A farsighted person cannot see close objects clearly,
because images are focused behind the retina. A convex
lens corrects this defect.
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
A flashlight beam is directed at a swimming pool in the
dark at an angle of 46° with respect to the normal to the
surface of water. What is the angle of refraction of the
beam in the water? (The refractive index for water is
1.33.)
A. 18°
B. 30°
C. 33°
D. 44°
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
The speed of light in diamond is 1.24×108 m/s.
What is the index of refraction of diamond?
A. 0.0422
B. 0.413
C. 1.24
D. 2.42
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
Which one of the items below is not involved in
the formation of rainbows?
A. diffraction
B. dispersion
C. reflection
D. refraction
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
George’s picture is being
taken by Cami, as shown in
the figure, using a camera
which has a convex lens with
a focal length of 0.0470 m.
Determine George’s image
position.
A. 1.86 cm
C. 4.82 cm
B. 4.70 cm
D. 20.7 cm
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
What is the magnification of an object that is
4.15 m in front of a camera that has an image
position of 5.0 cm?
A. -0.83
B. -0.012
C. 0.83
D. 1.2
CHAPTER
18
Refraction and Lenses
Standardized Test Practice
Test-Taking Tip
Use as Much Time as You Can
You will not get extra points for finishing a test early.
Work slowly and carefully to prevent careless errors
that can occur when you are hurrying to finish.
CHAPTER
18
Refraction and Lenses
Chapter Resources
Indices of Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
Angle of Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
Wave Model of Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
Understanding Total Internal Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
Optical Fibers as an Application of Total
Internal Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
Mirages
CHAPTER
18
Refraction and Lenses
Chapter Resources
Dispersion of Light
CHAPTER
18
Refraction and Lenses
Chapter Resources
Formation of Rainbows
CHAPTER
18
Refraction and Lenses
Chapter Resources
Convex and Concave Lens
Horizons Companies
Horizons Companies
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Focal Point of a Lens
CHAPTER
18
Refraction and Lenses
Chapter Resources
An Object Placed at Twice the Focal
Length from the Lens
CHAPTER
18
Refraction and Lenses
Chapter Resources
Chromatic Aberration of a Simple Lens
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Cross Sections of Four Different Thin
Lenses
CHAPTER
18
Refraction and Lenses
Chapter Resources
An Air Lens Constructed of Two Watch
Glasses
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Human Eye
CHAPTER
18
Refraction and Lenses
Chapter Resources
Nearsightedness and Farsightedness
CHAPTER
18
Refraction and Lenses
Chapter Resources
A Ray of Light Strikes the Interface
between the Air and a Person’s Cornea
CHAPTER
18
Refraction and Lenses
Chapter Resources
An Astronomical Refracting Telescope
CHAPTER
18
Refraction and Lenses
Chapter Resources
A Typical Binocular Design
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Optical System Used in a Single-lens
Reflex Camera
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Optical System Used in a Simple
Compound Microscope
CHAPTER
18
Refraction and Lenses
Chapter Resources
Concept Mapping
CHAPTER
18
Refraction and Lenses
Chapter Resources
Determining Whether Substance A or B
has a Larger Index of Refraction
CHAPTER
18
Refraction and Lenses
Chapter Resources
A Ray of Light Travelling from Air into a
Liquid
CHAPTER
18
Refraction and Lenses
Chapter Resources
Swimming Pool Lights
CHAPTER
18
Refraction and Lenses
Chapter Resources
A Ray of Light
CHAPTER
18
Refraction and Lenses
Chapter Resources
A Light Ray Enters a Block of Crown
Glass
CHAPTER
18
Refraction and Lenses
Chapter Resources
Sunlight Reflects Diffusively off the
Bottom of an Aquarium
CHAPTER
18
Refraction and Lenses
Chapter Resources
The Adjacent Sides of a Square Block of
Glass
CHAPTER
18
Refraction and Lenses
Chapter Resources
Determining George’s Image Position
CHAPTER
18
Refraction and Lenses
Chapter Resources
Determining the Image Position
CHAPTER
18
Refraction and Lenses
Chapter Resources
Angle of Refraction
A light beam in air hits a sheet of crown glass at
an angle of 30.0°. At what angle is the light beam
refracted?
CHAPTER
18
Refraction and Lenses
Chapter Resources
An Image Formed by a Convex Lens
An object is placed 32.0 cm from a convex lens
that has a focal length of 8.0 cm.
a. Where is the image?
b. If the object is 3.0 cm high, how high is the
image?
c. What is the orientation of the image?
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